Harlow Shapley: Spiral nebulae are nearby members of our Galaxy.

• Novae (Nova Review)
  
Novae had been seen in the Andromeda Nebula. If the Andromeda Nebula was as large as the Milky Way, its distance would be immense and the novae which had been observed would have luminosities much greater than those in the Milky Way.

Problem: Remember, Shapley thought the Milky Way was much bigger than it actually is. He had based his estimates of the Milky Way's size on his distances to globular clusters, and at the time it was not understood that dust was affecting those measurements. Since Shapley thought the Milky Way was really big, if Andromeda had to be that big too, given its measured angular size, it would have to bereally far away. In fact, Andromeda isn't that big, and isnt that far away, and so the luminosities of the novae don't need to be that large to be seen.
 
 
• Rotation
Adrian van Maanen had observed proper motion of objects in the spiral nebula M101. If M101 was as big as the Milky Way, its outer edge would be moving at a fantastic velocity. van Maanen's data indicated that M101 rotated once every 65 million years. If so, the outer edge of M101 would be rotating at nearly 5,000 km/s, much faster than the Milky Way's rotation speed of 220 km/s.

Problem: van Maanen's measurements were simply wrong.

• Novae
If the Andromeda nebula were within our own Galaxy, its novae would have luminosities much less than the other novae in our Galaxy.
 
• Radial velocities
Most of the spiral nebulae have very large radial velocities (>1000 km/s). How then could they remain part of the Milky Way -- they should escape.

Also, if they were nearby and moving that fast, the nebulae themselves should have large proper motions. We don't see that.